Unlikely Newton polygons and Ekedahl–Oort types for abelian covers

Let $g \geq 18$, and let $m$ be the least common multiple of the exponents of all of the Galois groups of abelian covers of $\mathbf{P}^1$ branched at three points of genus $g$. Unlikely-types conjecture. If $p$ is a prime such that $p \not \equiv 1$ modulo $m$, then there exist abelian covers $X_1$ and $X_2$ of $\mathbf{P}^1$ branched at three points defined over $\overline{\mathbf{F}_p}$ such that $X_1$ has an unlikely Newton polygon and $X_2$ has an unlikely Ekedahl–Oort type. The computational evidence suggests that unlikely Newton polygons and Ekedahl–Oort types occur frequently in this family, but the assertion for every prime satisfying the stated congruence condition remains open.